WI France keeps on Fighting

I really don't see how the French could hold any part of actual France, even if they decide to fight to the bitter end... the Germans simply had too much for them to handle, and had captured too much already. All you would end up with is a more devestated France, Germans occupying all of France (no Vichy), and a few more dead germans who couldn't take part in Barbarossa. N. Africa is their best hope for continued resistance....
It may not have been completely impossible to put out a defense in Provence behind the Rhone and the Alps. That could have been a formidable redoubt. Obviously, this requires sacrificing cities like Lyons and Marseilles. Also, to pull that off, you may want an earlier retreat of the armies garrisoning the Maginot line.

The French also had a plan for forganizing a redoubt behind the Gironde and the Montagne Noire in the Southwest. Doesn't seem very strategic to me.
Fortress Brittany

Another plan was this - seat the French government in Rennes and fortify the Peninsula. Weygand, Georges and Alan Brooke made some discussions on the subject and thought it viable, but Alan Brooke told the War Cabinet that the plan in his wiev was unfeasiable. According to Robert Aron De Gaulle was going to London to get the Brits cooperation on Fortress Brittany.
Depends. Was the French military still using Druidic potions at the time?

I don't know about that, but in OTL the UK sent the 51st Highland Division into northern France in a desperate effort to shore up French forces, and everyone knows what kind of marvellous potions and elixars we Scots use!
Is there any plausible way that even a small part of France could have held out from the actual German invasion during WWII? I'm not talking about Vichy France, but a part of France that remains at war with the Germans until Liberation of the rest in 1944.

According to "A Guide to World War II for Dummies", France was a great military power in 1940, and should've gave the Germans a heck of a fight, if the French military and government weren't so demoralized and surprised (Ardennes, anyone?). The German army, for all of its glory, would've become hard-pressed if the French had offered even the smallest resistance...